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Math Help - help with integrating factor equation

  1. #1
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    help with integrating factor equation

    hi

    i have been given the attached question to work through and i just cant get my head around it (sorry its an attachment, i can not work out how to display it within this message).

    any help/pointers you could give would be great

    thanks
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by wallsst View Post
    hi

    i have been given the attached question to work through and i just cant get my head around it (sorry its an attachment, i can not work out how to display it within this message).

    any help/pointers you could give would be great

    thanks
    i think, there was a mistake.. Q is not 2.5t but (5-2.5t)

    anyways, i'll put a solution here..

    i have to find the temp at time T if T=60^o when t=0 using \frac{dT}{dt} + 0.1T = e^{0.1t}
    and the integrating factor is given by  = \exp \left[ {\int_0^t {0.1 \, d\tau}} \right] = \exp (0.1t) = e^{0.1t}

    so, T= \dfrac{1}{e^{0.1t}} \left( {60^o + \int_0^t e^{0.1\tau }\left( {5-2.5\tau } \right)} \, d\tau \right)

    the integral part can be solved using integration by parts once..
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  3. #3
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    thanks, after a few hours of looking at it, it did finally click and, as you said, Q is (5-2.5t)

    cheers for the help
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